There are many common mathematics mistakes that students frequently make in exams. Often, students think they don’t really matter, because usually, they only cost you a mark. I mean, who cares about one mark right?
The thing is, marks add up. A sign error here, forgetting a unit there; before you know it you are losing enough marks to drop you from a Band 6 to a Band 5. Or a Band 5 to a Band 4. How would you feel if you got a 79 in your Trial, and you lost a mark because you forgot the integration constant! I’ve been there, done that, and it isn’t a nice feeling.
With that in mind, let’s go through the common mathematics mistakes to look out for, especially in pressure exam situations!
1. Sign Errors
We’ll begin with one of the most common mathematics mistakes that everyone will know about. Sign errors are the bane of a Math student’s existence. You could very easily lose 5+ marks to sign errors in your HSC Exam. Most commonly, this pops up when you are subtracting a multi-term expressions.
To minimise the chance of sign errors, you need to write all your lines of working. Trying to multitask increases the chance of making a silly error. Be especially careful when expanding brackets.
2. Incorrect Form/Units
Not putting your answers in the correct form affects numerous areas of the Mathematics course. Using radians instead of degrees, giving an equation in gradient-intercept form when general form is specifically requested, incorrect number of decimal points, etc. Make sure to address the specific question and put your answer in the correct form. There is nothing more frustrating than losing a mark because you didn’t convert your answer from meters to kilometers (and yes, you would lose a mark for this). In terms of common mathematics mistakes, this is one of the most frustrating; don’t fall for it!
3. Integration Constant and Notation (My Most Common Mathematics Mistakes)
We’ve all been guilty of this at some point (or maybe I was just especially bad at it).Two things to remember:
a) Remember the ‘dx’ or ‘dy’ at the end of your integral. This may not cost you a mark, but it very well could, so don’t risk it. I made this mistake all the time.
b) Make sure you remember to put the integration constant for indefinite integrals. This will definitely cost you a mark, and every year the marking center warns us about it, it is one of the most common mathematics mistakes. Don’t forget it!
4. Not Testing Nature of Points
This is a common error, especially under pressure. Remember that you MUST test the nature of stationary points, using either the ‘point either side’ method, or more commonly, the ‘second derivative’ test. Further, you also MUST test your points of inflexion using the ‘point either side’ method. Not doing so will cost you a mark. Consider the las question from my HSC (the scenario itself isn’t important):
Find the values of x and y that maximize the amount of light coming through the window under test conditions.
Many students found a value of x and y which gave a stationary point, but did not prove it was a maximum! Just because the question says you are looking for a maximum, you cannot overlook these texts.
5. Eliminating Solutions by Dividing by Zero
See if you can catch what is wrong with my solution to this trigonometric equation.
Looks okay, but look at the first step. We divide by sinx. What if sinx had been equal to zero, we have removed some solutions! The correct method is instead to factorise the sinx out of the expression, which will give additional solutions.
Make sure that you only divide by valid constant terms, and factorize pro-numerals/unknown expressions. This will ensure you never lose any solutions.
6. Not Fully Simplifying/Factorizing
An extremely common mistake in exams is not expressing the solution in the simplest possible form. This may involve simplifying a fraction, grouping like terms, or rationalizing a denominator, among others. This also includes not fully factorizing a solution, when required.
Make sure you take 5 seconds to check for these sorts of mistakes. For factorizing questions, check how many marks it is worth. If you have done 1 line of working for 3 marks, chances are there is more to be done.
7. Rounding Too Early
This one is simple; never round any values until the final answer. Or, if you do, make sure you take enough decimal places (I used to take four by default). I could go into the proper theory behind how many points to take, based on the error in the values and the question (first year university students who take Physics will know all about this), but it’s much easier to just give a blanket rule. Round only at the end, and use your calculator to store preliminary values.
8. Taking a Question ‘Too Far’
Many students will look at a question and just start working based on what they assume the question to be. Then, they read it back and go: “Oh, I only had to find the first maximum value, not all three.” Or, “Hmm, I didn’t even have to find inflexion points here…”
Make sure you only do the work required for a question. Part of this comes from experience, knowing exactly the data you need for an answer. For more difficult questions, some aimless working may be inevitable. However, minimize wasted time by reading a question fully before commencing work. It seems like a silly reminder, but exams are pressure scenarios, and common sense can sometimes fall out the window.
9. Incorrect Assumptions
This primarily concerns geometry questions, though it can apply for calculus questions, probability questions, and a few other areas: Never make any assumptions based on what the diagram looks like! Unless it specifically says that angle ABC is a right angle, then it isn’t a right angle until you prove it. Unless it says that three points are collinear, then they aren’t collinear until you prove it. Use only the information given to you, never create your own.
10. Square Rooting Sign Errors
Another common mistake. Make sure that when you square root (or any even power) a value, you acknowledge that it can be either a positive or negative result. Even if the answer could only be positive (EG – it is a distance value from the Pythagorean formula), you absolutely must acknowledge the negative answer, then disregard it based on the situation at hand. Also remember that you can’t square root a negative number (unless you are a 4 Unit Student, in which case you can, but 2U students need not worry about such complex things).
11. Diagrams!
This is a big area that is identified by the Marking Centre every year. Make sure your diagrams are clear, labelled, and take up at least a third of the page. No more to be said here, just give the diagrams time and space and they are (normally) easy marks to be had.
12. Forgetting to Swap the Inequality Sign
Finally, don’t forget to swap the sign of an inequality when you multiply or divide by a negative. This should be second nature, but there is always somebody who forgets. Don’t be that person.
On inspection of the HSC Papers for 2014 and 2015, these errors had the potential to pop up at least once, and usually, multiple times. This could cost you upwards of a dozen marks in your HSC.
My biggest tip to avoid these unnecessary mark losses in any Mathematics exam is to take your time. Move carefully through the questions, don’t rush, it will cause silly mistakes.
If you know of any other traps, feel free to share them in the comments below! 
